{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "source": [
    "import numpy as np\r\n",
    "import pandas as pd\r\n",
    "import matplotlib.pyplot as plt"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "Matplotlib is building the font cache; this may take a moment.\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "source": [
    "ex0=pd.read_table('ex0.txt',header=None)\r\n",
    "ex0.head()"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "     0         1         2\n",
       "0  1.0  0.067732  3.176513\n",
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       "2  1.0  0.995731  4.550095\n",
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       "      <td>1.0</td>\n",
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     "metadata": {},
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    }
   ],
   "metadata": {}
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  {
   "cell_type": "code",
   "execution_count": 3,
   "source": [
    "'''\r\n",
    "工具函数：数据集转 - 矩阵\r\n",
    "'''\r\n",
    "\r\n",
    "def get_mat(df):\r\n",
    "    #特征矩阵\r\n",
    "    xMat = np.mat(df.iloc[:,:-1])\r\n",
    "    #值矩阵（转换成 列向量）\r\n",
    "    yMat = np.mat(df.iloc[:,-1]).T\r\n",
    "\r\n",
    "    return xMat,yMat"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "source": [
    "def plot_df(df):\r\n",
    "    xMat,yMat= get_mat(df)\r\n",
    "    plt.scatter(xMat.A[:,1],yMat.A,c='r',s=5)\r\n",
    "    plt.show()"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "source": [
    "plot_df(ex0)"
   ],
   "outputs": [
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "source": [
    "def stand_regression(df):\r\n",
    "    xMat,yMat = get_mat(df)\r\n",
    "    xTx = xMat.T*xMat\r\n",
    "    #判断是否为奇异矩阵\r\n",
    "    if np.linalg.det(xTx) ==0:\r\n",
    "        print('奇异矩阵，无法求逆')\r\n",
    "        return\r\n",
    "    \r\n",
    "    ws = xTx.I *(xMat.T * yMat)\r\n",
    "    return ws"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "stand_regression(ex0)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "matrix([[3.00774324],\n",
       "        [1.69532264]])"
      ]
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "source": [
    "def plotReg(df):\r\n",
    "    xMat,yMat = get_mat(df)\r\n",
    "    #绘制数据集\r\n",
    "    plt.scatter(xMat.A[:,1],yMat.A,c='r',s=5)\r\n",
    "    #求解线性回归方程\r\n",
    "    ws = stand_regression(df)\r\n",
    "    yHat = xMat *ws\r\n",
    "    #绘制\r\n",
    "    plt.plot(xMat[:,1],yHat,c='g')\r\n",
    "    plt.show()"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "source": [
    "plotReg(ex0)"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### 局部加权线性回归函数"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "source": [
    "def lwlr(testMat,xMat,yMat,k=1.0):\r\n",
    "    #测 矩阵行数\r\n",
    "    n = testMat.shape[0]\r\n",
    "    #输入 矩阵行数\r\n",
    "    m = xMat.shape[0]\r\n",
    "    #初始化 Weight\r\n",
    "    w = np.mat(np.eye(m))\r\n",
    "    yHat = np.zeros(n)\r\n",
    "\r\n",
    "    for i in range(n):\r\n",
    "        for j in range(m):\r\n",
    "            diffMat = testMat[i] - xMat[j]\r\n",
    "            w[j,j] = np.exp(diffMat*diffMat.T/(-2*k**2))\r\n",
    "        xTx = xMat.T*(w*xMat)\r\n",
    "        if np.linalg.det(xTx) == 0:\r\n",
    "            print(\"奇异矩阵无法求逆\")\r\n",
    "            return\r\n",
    "        ws = xTx.I * (xMat.T*(w*yMat))\r\n",
    "        yHat[i] = testMat[i] * ws\r\n",
    "    return ws,yHat"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "source": [
    "def pl_lwlr(df,k=1.0):\r\n",
    "    xMat,yMat = get_mat(df)\r\n",
    "    srtInd = xMat[:,1].argsort(0)\r\n",
    "    xSort = xMat[srtInd][:,0]\r\n",
    "\r\n",
    "    _,yHat = lwlr(xMat,xMat,yMat,k)\r\n",
    "    \r\n",
    "    #绘制\r\n",
    "    fig = plt.figure(figsize=(10,8),dpi=100)\r\n",
    "    fig1 =fig.add_subplot(111)\r\n",
    "     #绘制数据集\r\n",
    "    plt.scatter(xMat.A[:,1],yMat.A,c='r',s=5)\r\n",
    "    #求解回归方程\r\n",
    "    plt.plot(xSort[:,1],yHat[srtInd],linewidth=1,c='b')\r\n",
    "    "
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "source": [
    "pl_lwlr(ex0,0.01)"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
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"
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